Yes, the sine wave does represent the amplitude of a circle, however, when shown over time, the phasor turns into a sine wave. The phasor only exists in pure math: it is always with respect to time when it is the real world.

probably because I'm really tired but at first I thought the sticks made the music somehow :p

But that gave me an idea, you should totally put a keyboard under there :p It will play the same tune over and over again but who cares it would be awesome ^^ And I think you can rig the 'fingers" easily to play the note you want when you want :)